Analysis of the plastic zone near the crack tips under the uniaxial tension using ordinary state‐based peridynamics

Abstract

In this paper, the plastic model of ordinary state‐based peridynamics is established. The size and shape of plastic zone around crack tips with the different inclination angles are simulated using ordinary state‐based peridynamics. Comparison of the size and shape of plastic zone around the crack tips obtained from peridynamic solution and analytic solution is made. It is found that the relative errors between the analytical and peridynamic solution are very little. Therefore, it is feasible to predict the plastic zone around crack tips using ordinary state‐based peridynamics.

An ordinary state-based peridynamic elastoplastic 2D model consistent with J2 plasticity

“…For elastoplastic behavior, OSB-PD models have been introduced in (Madenci and Oterkus, 2016;Mitchell, 2011;Silling et al, 2007). Several 2D versions of this theory appeared in (Madenci and Oterkus, 2016;Pashazad and Kharazi, 2019;Zhou et al, 2018).…”

“…Another limitation of the models in (Madenci and Oterkus, 2016;Pashazad and Kharazi, 2019) is that they are not valid under arbitrary rigid-body rotations (Le and Bobaru, 2018;Madenci, 2017). Estimation of the plastic zone near the crack tips in rocks was studied in (Zhou et al, 2018) using a 2D OSB-PD model. The 2D formulation in (Zhou et al, 2018), adopts the 3D formulation suggested in (Mitchell et al, 2015).…”

“…Estimation of the plastic zone near the crack tips in rocks was studied in (Zhou et al, 2018) using a 2D OSB-PD model. The 2D formulation in (Zhou et al, 2018), adopts the 3D formulation suggested in (Mitchell et al, 2015). However, as we discuss in detail in section 3, the approach in (Zhou et al, 2018) does not lead to a correct two-dimensional decomposition for the extension and force states, since the stress tensors corresponding to their decomposed force states are not consistent with the classical decomposition of stress which would lead to an incorrect yield function.…”

“…The 2D formulation in (Zhou et al, 2018), adopts the 3D formulation suggested in (Mitchell et al, 2015). However, as we discuss in detail in section 3, the approach in (Zhou et al, 2018) does not lead to a correct two-dimensional decomposition for the extension and force states, since the stress tensors corresponding to their decomposed force states are not consistent with the classical decomposition of stress which would lead to an incorrect yield function. Moreover, it is not clear if the 2D formulation in (Mitchell et al, 2015) is for plane stress or plane strain conditions.…”

A nonlocal energy‐informed neural network for isotropic elastic solids with cracks under thermomechanical loads

“…The SB‐PD formulation can be classified into the ordinary state‐based peridynmaics (OSB‐PD) 12,13 and non‐ordinary state‐based peridynmaics (NOSB‐PD), 14–17 according to whether the force density vector state is parallel to the deformation vector state. The OSB‐PD is an active area of research and has been a promising framework for modeling various problems 18–22 …”